A289368 Coefficients in expansion of (E_6^2/E_4^3)^(1/24).

1, -72, -6048, -4217184, -1264437504, -606533479920, -251777443450752, -117085712395216320, -53634689421870422016, -25408429618361083967592, -12110787335129301116994240, -5854620911089647830793873696

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..367

Formula

G.f.: (1 - 1728/j)^(1/24).

G.f.: Product_{n>=1} (1-q^n)^(12*A289367(n)).

a(n) ~ c * exp(2*Pi*n) / n^(13/12), where c = -Gamma(1/4)^(1/3) / (2^(7/3) * 3^(23/24) * Pi^(1/4) * Gamma(11/12)) = -0.07569217204117312767729284017524325060022536591050774997610261275428... - Vaclav Kotesovec, Jul 08 2017, updated Mar 04 2018

a(n) * A289369(n) ~ -(sqrt(3)-1) * exp(4*Pi*n) / (24*sqrt(2)*Pi*n^2). - Vaclav Kotesovec, Mar 04 2018

Mathematica

nmax = 20; CoefficientList[Series[((1 - 504*Sum[DivisorSigma[5, k]*x^k, {k, 1, nmax}])^2 / (1 + 240*Sum[DivisorSigma[3, k]*x^k, {k, 1, nmax}])^3)^(1/24), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)

Crossrefs

(E_6^2/E_4^3)^(k/288): A289366 (k=1), A296609 (k=2), A296614 (k=3), A296652 (k=4), A297021 (k=6), A299422 (k=8), A299862 (k=9), this sequence (k=12), A299856 (k=16), A299857 (k=18), A299858 (k=24), A299863 (k=32), A299859 (k=36), A299860 (k=48), A299861 (k=72), A299414 (k=96), A299413 (k=144), A289210 (k=288).

Cf. A000521 (j), A108091 (E_4^(1/8)), A109817 (E_6^(1/12)).

Cf. A289366, A289367, A294974, A294976.

Sequence in context: A358116 A216705 A223148 * A334357 A119750 A283093

Adjacent sequences: A289365 A289366 A289367 * A289369 A289370 A289371

Keyword

sign

Author

Seiichi Manyama, Jul 04 2017

Status

approved